If the difference between CI and SI on a certain sum at

If the difference between CI and SI on a certain sum at r% per annum for 3 years is Rs x, find the expression for the principal sum. If the difference between CI and SI on a certain sum at 4% for 3 years is Rs. 608. Find the sum.

Let the sum be ₹ P and rate = r%
Here , t = 3 years

SI =	Pr × 3	=	3 Pr
	100		100

C.I. = P			1 +	r		³	− 1
				100

CI = P		1 +	r³	+	3r²	+	3r	− 1
			100³		100²		100

CI = P		r³	+	3r²	+	3r
		100³		100²		100

⇒ CI – SI ( D ) = P		r³	+	3r²	+	3r		−	3Pr
		100³		100²		100			100

D = P		r³	+	3r²
		100³		100²

D = P		r²		[r + 300]
		100³

P =	D (100)³
	r²(r + 300)

Given Here, D = ₹ 608 and r = 4% per annum

P =	608 × 100 × 100 × 100
	4 × 4 × (4 + 300)

P = Rs. 1,25,000.